{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "leading-fusion",
   "metadata": {},
   "source": [
    "# 习题 4.5\n",
    "\n",
    "![习题 4.5](https://tva1.sinaimg.cn/large/008i3skNly1gr9qnd43plj31a40hun3k.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "straight-notice",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 30 × 8</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>X3</th><th scope=col>X4</th><th scope=col>X5</th><th scope=col>X6</th><th scope=col>X7</th><th scope=col>X8</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>山西</th><td> 8.35</td><td>23.53</td><td> 7.51</td><td> 8.62</td><td>17.42</td><td>10.00</td><td>1.04</td><td>11.21</td></tr>\n",
       "\t<tr><th scope=row>内蒙古</th><td> 9.25</td><td>23.75</td><td> 6.61</td><td> 9.19</td><td>17.77</td><td>10.48</td><td>1.72</td><td>10.51</td></tr>\n",
       "\t<tr><th scope=row>吉林</th><td> 8.19</td><td>30.50</td><td> 4.72</td><td> 9.78</td><td>16.28</td><td> 7.60</td><td>2.52</td><td>10.32</td></tr>\n",
       "\t<tr><th scope=row>黑龙江</th><td> 7.73</td><td>29.20</td><td> 5.42</td><td> 9.43</td><td>19.29</td><td> 8.49</td><td>2.52</td><td>10.00</td></tr>\n",
       "\t<tr><th scope=row>河南</th><td> 9.42</td><td>27.93</td><td> 8.20</td><td> 8.14</td><td>16.17</td><td> 9.42</td><td>1.55</td><td> 9.76</td></tr>\n",
       "\t<tr><th scope=row>甘肃</th><td> 9.16</td><td>27.98</td><td> 9.01</td><td> 9.32</td><td>15.99</td><td> 9.10</td><td>1.82</td><td>11.35</td></tr>\n",
       "\t<tr><th scope=row>青海</th><td>10.06</td><td>28.64</td><td>10.52</td><td>10.05</td><td>16.18</td><td> 8.39</td><td>1.96</td><td>10.81</td></tr>\n",
       "\t<tr><th scope=row>河北</th><td> 9.09</td><td>28.12</td><td> 7.40</td><td> 9.62</td><td>17.26</td><td>11.12</td><td>2.49</td><td>12.65</td></tr>\n",
       "\t<tr><th scope=row>陕西</th><td> 9.41</td><td>28.20</td><td> 5.77</td><td>10.80</td><td>16.36</td><td>11.56</td><td>1.53</td><td>12.17</td></tr>\n",
       "\t<tr><th scope=row>宁夏</th><td> 8.70</td><td>28.12</td><td> 7.21</td><td>10.53</td><td>19.45</td><td>13.30</td><td>1.66</td><td>11.96</td></tr>\n",
       "\t<tr><th scope=row>新疆</th><td> 6.93</td><td>29.85</td><td> 4.54</td><td> 9.49</td><td>16.62</td><td>10.65</td><td>1.88</td><td>13.61</td></tr>\n",
       "\t<tr><th scope=row>湖北</th><td> 8.67</td><td>36.05</td><td> 7.31</td><td> 7.75</td><td>16.67</td><td>11.68</td><td>2.38</td><td>12.88</td></tr>\n",
       "\t<tr><th scope=row>云南</th><td> 9.98</td><td>37.69</td><td> 7.01</td><td> 8.94</td><td>16.15</td><td>11.08</td><td>0.83</td><td>11.67</td></tr>\n",
       "\t<tr><th scope=row>湖南</th><td> 6.77</td><td>38.69</td><td> 6.01</td><td> 8.82</td><td>14.79</td><td>11.44</td><td>1.74</td><td>13.23</td></tr>\n",
       "\t<tr><th scope=row>安徽</th><td> 8.14</td><td>37.75</td><td> 9.61</td><td> 8.49</td><td>13.15</td><td> 9.76</td><td>1.28</td><td>11.28</td></tr>\n",
       "\t<tr><th scope=row>贵州</th><td> 7.67</td><td>35.71</td><td> 8.04</td><td> 8.31</td><td>15.13</td><td> 7.76</td><td>1.41</td><td>13.25</td></tr>\n",
       "\t<tr><th scope=row>辽宁</th><td> 7.90</td><td>39.77</td><td> 8.49</td><td>12.94</td><td>19.27</td><td>11.05</td><td>2.04</td><td>13.29</td></tr>\n",
       "\t<tr><th scope=row>四川</th><td> 7.18</td><td>40.91</td><td> 7.32</td><td> 8.94</td><td>17.60</td><td>12.75</td><td>1.14</td><td>14.80</td></tr>\n",
       "\t<tr><th scope=row>山东</th><td> 8.82</td><td>33.70</td><td> 7.59</td><td>10.98</td><td>18.82</td><td>14.73</td><td>1.78</td><td>10.10</td></tr>\n",
       "\t<tr><th scope=row>江西</th><td> 6.25</td><td>35.02</td><td> 4.72</td><td> 6.28</td><td>10.03</td><td> 7.15</td><td>1.93</td><td>10.39</td></tr>\n",
       "\t<tr><th scope=row>福建</th><td>10.60</td><td>52.41</td><td> 7.70</td><td> 9.98</td><td>12.53</td><td>11.70</td><td>2.31</td><td>14.69</td></tr>\n",
       "\t<tr><th scope=row>广西</th><td> 7.27</td><td>52.65</td><td> 3.84</td><td> 9.16</td><td>13.03</td><td>15.26</td><td>1.98</td><td>14.57</td></tr>\n",
       "\t<tr><th scope=row>海南</th><td>13.45</td><td>55.85</td><td> 5.50</td><td> 7.45</td><td> 9.55</td><td> 9.52</td><td>2.21</td><td>16.30</td></tr>\n",
       "\t<tr><th scope=row>天津</th><td>10.85</td><td>44.68</td><td> 7.32</td><td>14.51</td><td>17.13</td><td>12.08</td><td>1.26</td><td>11.57</td></tr>\n",
       "\t<tr><th scope=row>江苏</th><td> 7.21</td><td>45.79</td><td> 7.66</td><td>10.36</td><td>16.56</td><td>12.86</td><td>2.25</td><td>11.69</td></tr>\n",
       "\t<tr><th scope=row>浙江</th><td> 7.68</td><td>50.37</td><td>11.35</td><td>13.30</td><td>19.25</td><td>14.59</td><td>2.75</td><td>14.87</td></tr>\n",
       "\t<tr><th scope=row>北京</th><td> 7.78</td><td>48.44</td><td> 8.00</td><td>20.51</td><td>22.12</td><td>15.73</td><td>1.15</td><td>16.61</td></tr>\n",
       "\t<tr><th scope=row>西藏</th><td> 7.94</td><td>39.65</td><td>20.97</td><td>20.82</td><td>22.52</td><td>12.41</td><td>1.75</td><td> 7.90</td></tr>\n",
       "\t<tr><th scope=row>上海</th><td> 8.28</td><td>64.34</td><td> 8.00</td><td>22.22</td><td>20.06</td><td>15.12</td><td>0.72</td><td>22.89</td></tr>\n",
       "\t<tr><th scope=row>广东</th><td>12.47</td><td>76.39</td><td> 5.52</td><td>11.24</td><td>14.52</td><td>22.00</td><td>5.46</td><td>25.50</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 30 × 8\n",
       "\\begin{tabular}{r|llllllll}\n",
       "  & X1 & X2 & X3 & X4 & X5 & X6 & X7 & X8\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t山西 &  8.35 & 23.53 &  7.51 &  8.62 & 17.42 & 10.00 & 1.04 & 11.21\\\\\n",
       "\t内蒙古 &  9.25 & 23.75 &  6.61 &  9.19 & 17.77 & 10.48 & 1.72 & 10.51\\\\\n",
       "\t吉林 &  8.19 & 30.50 &  4.72 &  9.78 & 16.28 &  7.60 & 2.52 & 10.32\\\\\n",
       "\t黑龙江 &  7.73 & 29.20 &  5.42 &  9.43 & 19.29 &  8.49 & 2.52 & 10.00\\\\\n",
       "\t河南 &  9.42 & 27.93 &  8.20 &  8.14 & 16.17 &  9.42 & 1.55 &  9.76\\\\\n",
       "\t甘肃 &  9.16 & 27.98 &  9.01 &  9.32 & 15.99 &  9.10 & 1.82 & 11.35\\\\\n",
       "\t青海 & 10.06 & 28.64 & 10.52 & 10.05 & 16.18 &  8.39 & 1.96 & 10.81\\\\\n",
       "\t河北 &  9.09 & 28.12 &  7.40 &  9.62 & 17.26 & 11.12 & 2.49 & 12.65\\\\\n",
       "\t陕西 &  9.41 & 28.20 &  5.77 & 10.80 & 16.36 & 11.56 & 1.53 & 12.17\\\\\n",
       "\t宁夏 &  8.70 & 28.12 &  7.21 & 10.53 & 19.45 & 13.30 & 1.66 & 11.96\\\\\n",
       "\t新疆 &  6.93 & 29.85 &  4.54 &  9.49 & 16.62 & 10.65 & 1.88 & 13.61\\\\\n",
       "\t湖北 &  8.67 & 36.05 &  7.31 &  7.75 & 16.67 & 11.68 & 2.38 & 12.88\\\\\n",
       "\t云南 &  9.98 & 37.69 &  7.01 &  8.94 & 16.15 & 11.08 & 0.83 & 11.67\\\\\n",
       "\t湖南 &  6.77 & 38.69 &  6.01 &  8.82 & 14.79 & 11.44 & 1.74 & 13.23\\\\\n",
       "\t安徽 &  8.14 & 37.75 &  9.61 &  8.49 & 13.15 &  9.76 & 1.28 & 11.28\\\\\n",
       "\t贵州 &  7.67 & 35.71 &  8.04 &  8.31 & 15.13 &  7.76 & 1.41 & 13.25\\\\\n",
       "\t辽宁 &  7.90 & 39.77 &  8.49 & 12.94 & 19.27 & 11.05 & 2.04 & 13.29\\\\\n",
       "\t四川 &  7.18 & 40.91 &  7.32 &  8.94 & 17.60 & 12.75 & 1.14 & 14.80\\\\\n",
       "\t山东 &  8.82 & 33.70 &  7.59 & 10.98 & 18.82 & 14.73 & 1.78 & 10.10\\\\\n",
       "\t江西 &  6.25 & 35.02 &  4.72 &  6.28 & 10.03 &  7.15 & 1.93 & 10.39\\\\\n",
       "\t福建 & 10.60 & 52.41 &  7.70 &  9.98 & 12.53 & 11.70 & 2.31 & 14.69\\\\\n",
       "\t广西 &  7.27 & 52.65 &  3.84 &  9.16 & 13.03 & 15.26 & 1.98 & 14.57\\\\\n",
       "\t海南 & 13.45 & 55.85 &  5.50 &  7.45 &  9.55 &  9.52 & 2.21 & 16.30\\\\\n",
       "\t天津 & 10.85 & 44.68 &  7.32 & 14.51 & 17.13 & 12.08 & 1.26 & 11.57\\\\\n",
       "\t江苏 &  7.21 & 45.79 &  7.66 & 10.36 & 16.56 & 12.86 & 2.25 & 11.69\\\\\n",
       "\t浙江 &  7.68 & 50.37 & 11.35 & 13.30 & 19.25 & 14.59 & 2.75 & 14.87\\\\\n",
       "\t北京 &  7.78 & 48.44 &  8.00 & 20.51 & 22.12 & 15.73 & 1.15 & 16.61\\\\\n",
       "\t西藏 &  7.94 & 39.65 & 20.97 & 20.82 & 22.52 & 12.41 & 1.75 &  7.90\\\\\n",
       "\t上海 &  8.28 & 64.34 &  8.00 & 22.22 & 20.06 & 15.12 & 0.72 & 22.89\\\\\n",
       "\t广东 & 12.47 & 76.39 &  5.52 & 11.24 & 14.52 & 22.00 & 5.46 & 25.50\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 30 × 8\n",
       "\n",
       "| <!--/--> | X1 &lt;dbl&gt; | X2 &lt;dbl&gt; | X3 &lt;dbl&gt; | X4 &lt;dbl&gt; | X5 &lt;dbl&gt; | X6 &lt;dbl&gt; | X7 &lt;dbl&gt; | X8 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 山西 |  8.35 | 23.53 |  7.51 |  8.62 | 17.42 | 10.00 | 1.04 | 11.21 |\n",
       "| 内蒙古 |  9.25 | 23.75 |  6.61 |  9.19 | 17.77 | 10.48 | 1.72 | 10.51 |\n",
       "| 吉林 |  8.19 | 30.50 |  4.72 |  9.78 | 16.28 |  7.60 | 2.52 | 10.32 |\n",
       "| 黑龙江 |  7.73 | 29.20 |  5.42 |  9.43 | 19.29 |  8.49 | 2.52 | 10.00 |\n",
       "| 河南 |  9.42 | 27.93 |  8.20 |  8.14 | 16.17 |  9.42 | 1.55 |  9.76 |\n",
       "| 甘肃 |  9.16 | 27.98 |  9.01 |  9.32 | 15.99 |  9.10 | 1.82 | 11.35 |\n",
       "| 青海 | 10.06 | 28.64 | 10.52 | 10.05 | 16.18 |  8.39 | 1.96 | 10.81 |\n",
       "| 河北 |  9.09 | 28.12 |  7.40 |  9.62 | 17.26 | 11.12 | 2.49 | 12.65 |\n",
       "| 陕西 |  9.41 | 28.20 |  5.77 | 10.80 | 16.36 | 11.56 | 1.53 | 12.17 |\n",
       "| 宁夏 |  8.70 | 28.12 |  7.21 | 10.53 | 19.45 | 13.30 | 1.66 | 11.96 |\n",
       "| 新疆 |  6.93 | 29.85 |  4.54 |  9.49 | 16.62 | 10.65 | 1.88 | 13.61 |\n",
       "| 湖北 |  8.67 | 36.05 |  7.31 |  7.75 | 16.67 | 11.68 | 2.38 | 12.88 |\n",
       "| 云南 |  9.98 | 37.69 |  7.01 |  8.94 | 16.15 | 11.08 | 0.83 | 11.67 |\n",
       "| 湖南 |  6.77 | 38.69 |  6.01 |  8.82 | 14.79 | 11.44 | 1.74 | 13.23 |\n",
       "| 安徽 |  8.14 | 37.75 |  9.61 |  8.49 | 13.15 |  9.76 | 1.28 | 11.28 |\n",
       "| 贵州 |  7.67 | 35.71 |  8.04 |  8.31 | 15.13 |  7.76 | 1.41 | 13.25 |\n",
       "| 辽宁 |  7.90 | 39.77 |  8.49 | 12.94 | 19.27 | 11.05 | 2.04 | 13.29 |\n",
       "| 四川 |  7.18 | 40.91 |  7.32 |  8.94 | 17.60 | 12.75 | 1.14 | 14.80 |\n",
       "| 山东 |  8.82 | 33.70 |  7.59 | 10.98 | 18.82 | 14.73 | 1.78 | 10.10 |\n",
       "| 江西 |  6.25 | 35.02 |  4.72 |  6.28 | 10.03 |  7.15 | 1.93 | 10.39 |\n",
       "| 福建 | 10.60 | 52.41 |  7.70 |  9.98 | 12.53 | 11.70 | 2.31 | 14.69 |\n",
       "| 广西 |  7.27 | 52.65 |  3.84 |  9.16 | 13.03 | 15.26 | 1.98 | 14.57 |\n",
       "| 海南 | 13.45 | 55.85 |  5.50 |  7.45 |  9.55 |  9.52 | 2.21 | 16.30 |\n",
       "| 天津 | 10.85 | 44.68 |  7.32 | 14.51 | 17.13 | 12.08 | 1.26 | 11.57 |\n",
       "| 江苏 |  7.21 | 45.79 |  7.66 | 10.36 | 16.56 | 12.86 | 2.25 | 11.69 |\n",
       "| 浙江 |  7.68 | 50.37 | 11.35 | 13.30 | 19.25 | 14.59 | 2.75 | 14.87 |\n",
       "| 北京 |  7.78 | 48.44 |  8.00 | 20.51 | 22.12 | 15.73 | 1.15 | 16.61 |\n",
       "| 西藏 |  7.94 | 39.65 | 20.97 | 20.82 | 22.52 | 12.41 | 1.75 |  7.90 |\n",
       "| 上海 |  8.28 | 64.34 |  8.00 | 22.22 | 20.06 | 15.12 | 0.72 | 22.89 |\n",
       "| 广东 | 12.47 | 76.39 |  5.52 | 11.24 | 14.52 | 22.00 | 5.46 | 25.50 |\n",
       "\n"
      ],
      "text/plain": [
       "                   X1    X2    X3    X4    X5    X6    X7   X8   \n",
       "\\u5c71\\u897f        8.35 23.53  7.51  8.62 17.42 10.00 1.04 11.21\n",
       "\\u5185\\u8499\\u53e4  9.25 23.75  6.61  9.19 17.77 10.48 1.72 10.51\n",
       "\\u5409\\u6797        8.19 30.50  4.72  9.78 16.28  7.60 2.52 10.32\n",
       "\\u9ed1\\u9f99\\u6c5f  7.73 29.20  5.42  9.43 19.29  8.49 2.52 10.00\n",
       "\\u6cb3\\u5357        9.42 27.93  8.20  8.14 16.17  9.42 1.55  9.76\n",
       "\\u7518\\u8083        9.16 27.98  9.01  9.32 15.99  9.10 1.82 11.35\n",
       "\\u9752\\u6d77       10.06 28.64 10.52 10.05 16.18  8.39 1.96 10.81\n",
       "\\u6cb3\\u5317        9.09 28.12  7.40  9.62 17.26 11.12 2.49 12.65\n",
       "\\u9655\\u897f        9.41 28.20  5.77 10.80 16.36 11.56 1.53 12.17\n",
       "\\u5b81\\u590f        8.70 28.12  7.21 10.53 19.45 13.30 1.66 11.96\n",
       "\\u65b0\\u7586        6.93 29.85  4.54  9.49 16.62 10.65 1.88 13.61\n",
       "\\u6e56\\u5317        8.67 36.05  7.31  7.75 16.67 11.68 2.38 12.88\n",
       "\\u4e91\\u5357        9.98 37.69  7.01  8.94 16.15 11.08 0.83 11.67\n",
       "\\u6e56\\u5357        6.77 38.69  6.01  8.82 14.79 11.44 1.74 13.23\n",
       "\\u5b89\\u5fbd        8.14 37.75  9.61  8.49 13.15  9.76 1.28 11.28\n",
       "\\u8d35\\u5dde        7.67 35.71  8.04  8.31 15.13  7.76 1.41 13.25\n",
       "\\u8fbd\\u5b81        7.90 39.77  8.49 12.94 19.27 11.05 2.04 13.29\n",
       "\\u56db\\u5ddd        7.18 40.91  7.32  8.94 17.60 12.75 1.14 14.80\n",
       "\\u5c71\\u4e1c        8.82 33.70  7.59 10.98 18.82 14.73 1.78 10.10\n",
       "\\u6c5f\\u897f        6.25 35.02  4.72  6.28 10.03  7.15 1.93 10.39\n",
       "\\u798f\\u5efa       10.60 52.41  7.70  9.98 12.53 11.70 2.31 14.69\n",
       "\\u5e7f\\u897f        7.27 52.65  3.84  9.16 13.03 15.26 1.98 14.57\n",
       "\\u6d77\\u5357       13.45 55.85  5.50  7.45  9.55  9.52 2.21 16.30\n",
       "\\u5929\\u6d25       10.85 44.68  7.32 14.51 17.13 12.08 1.26 11.57\n",
       "\\u6c5f\\u82cf        7.21 45.79  7.66 10.36 16.56 12.86 2.25 11.69\n",
       "\\u6d59\\u6c5f        7.68 50.37 11.35 13.30 19.25 14.59 2.75 14.87\n",
       "\\u5317\\u4eac        7.78 48.44  8.00 20.51 22.12 15.73 1.15 16.61\n",
       "\\u897f\\u85cf        7.94 39.65 20.97 20.82 22.52 12.41 1.75  7.90\n",
       "\\u4e0a\\u6d77        8.28 64.34  8.00 22.22 20.06 15.12 0.72 22.89\n",
       "\\u5e7f\\u4e1c       12.47 76.39  5.52 11.24 14.52 22.00 5.46 25.50"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data <- read.table(\"ex_4_5.utf8.txt\", head=TRUE); data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "flying-fifty",
   "metadata": {},
   "source": [
    "## (1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "detected-pakistan",
   "metadata": {},
   "source": [
    "在第一章中做过，用 cor 获取相关系数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "corrected-press",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 8 × 8 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>X3</th><th scope=col>X4</th><th scope=col>X5</th><th scope=col>X6</th><th scope=col>X7</th><th scope=col>X8</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td> 1.00000000</td><td> 0.33364671</td><td>-0.05453868</td><td>-0.06125369</td><td>-0.28936059</td><td>0.19879627</td><td> 0.3486985</td><td> 0.31867736</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td> 0.33364671</td><td> 1.00000000</td><td>-0.02290183</td><td> 0.39893102</td><td>-0.15630387</td><td>0.71113407</td><td> 0.4135946</td><td> 0.83495175</td></tr>\n",
       "\t<tr><th scope=row>X3</th><td>-0.05453868</td><td>-0.02290183</td><td> 1.00000000</td><td> 0.53332919</td><td> 0.49676279</td><td>0.03282961</td><td>-0.1390858</td><td>-0.25835810</td></tr>\n",
       "\t<tr><th scope=row>X4</th><td>-0.06125369</td><td> 0.39893102</td><td> 0.53332919</td><td> 1.00000000</td><td> 0.69842442</td><td>0.46791730</td><td>-0.1712742</td><td> 0.31275728</td></tr>\n",
       "\t<tr><th scope=row>X5</th><td>-0.28936059</td><td>-0.15630387</td><td> 0.49676279</td><td> 0.69842442</td><td> 1.00000000</td><td>0.28012915</td><td>-0.2082774</td><td>-0.08123414</td></tr>\n",
       "\t<tr><th scope=row>X6</th><td> 0.19879627</td><td> 0.71113407</td><td> 0.03282961</td><td> 0.46791730</td><td> 0.28012915</td><td>1.00000000</td><td> 0.4168213</td><td> 0.70158588</td></tr>\n",
       "\t<tr><th scope=row>X7</th><td> 0.34869847</td><td> 0.41359462</td><td>-0.13908580</td><td>-0.17127417</td><td>-0.20827738</td><td>0.41682128</td><td> 1.0000000</td><td> 0.39886792</td></tr>\n",
       "\t<tr><th scope=row>X8</th><td> 0.31867736</td><td> 0.83495175</td><td>-0.25835810</td><td> 0.31275728</td><td>-0.08123414</td><td>0.70158588</td><td> 0.3988679</td><td> 1.00000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 8 × 8 of type dbl\n",
       "\\begin{tabular}{r|llllllll}\n",
       "  & X1 & X2 & X3 & X4 & X5 & X6 & X7 & X8\\\\\n",
       "\\hline\n",
       "\tX1 &  1.00000000 &  0.33364671 & -0.05453868 & -0.06125369 & -0.28936059 & 0.19879627 &  0.3486985 &  0.31867736\\\\\n",
       "\tX2 &  0.33364671 &  1.00000000 & -0.02290183 &  0.39893102 & -0.15630387 & 0.71113407 &  0.4135946 &  0.83495175\\\\\n",
       "\tX3 & -0.05453868 & -0.02290183 &  1.00000000 &  0.53332919 &  0.49676279 & 0.03282961 & -0.1390858 & -0.25835810\\\\\n",
       "\tX4 & -0.06125369 &  0.39893102 &  0.53332919 &  1.00000000 &  0.69842442 & 0.46791730 & -0.1712742 &  0.31275728\\\\\n",
       "\tX5 & -0.28936059 & -0.15630387 &  0.49676279 &  0.69842442 &  1.00000000 & 0.28012915 & -0.2082774 & -0.08123414\\\\\n",
       "\tX6 &  0.19879627 &  0.71113407 &  0.03282961 &  0.46791730 &  0.28012915 & 1.00000000 &  0.4168213 &  0.70158588\\\\\n",
       "\tX7 &  0.34869847 &  0.41359462 & -0.13908580 & -0.17127417 & -0.20827738 & 0.41682128 &  1.0000000 &  0.39886792\\\\\n",
       "\tX8 &  0.31867736 &  0.83495175 & -0.25835810 &  0.31275728 & -0.08123414 & 0.70158588 &  0.3988679 &  1.00000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 8 × 8 of type dbl\n",
       "\n",
       "| <!--/--> | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| X1 |  1.00000000 |  0.33364671 | -0.05453868 | -0.06125369 | -0.28936059 | 0.19879627 |  0.3486985 |  0.31867736 |\n",
       "| X2 |  0.33364671 |  1.00000000 | -0.02290183 |  0.39893102 | -0.15630387 | 0.71113407 |  0.4135946 |  0.83495175 |\n",
       "| X3 | -0.05453868 | -0.02290183 |  1.00000000 |  0.53332919 |  0.49676279 | 0.03282961 | -0.1390858 | -0.25835810 |\n",
       "| X4 | -0.06125369 |  0.39893102 |  0.53332919 |  1.00000000 |  0.69842442 | 0.46791730 | -0.1712742 |  0.31275728 |\n",
       "| X5 | -0.28936059 | -0.15630387 |  0.49676279 |  0.69842442 |  1.00000000 | 0.28012915 | -0.2082774 | -0.08123414 |\n",
       "| X6 |  0.19879627 |  0.71113407 |  0.03282961 |  0.46791730 |  0.28012915 | 1.00000000 |  0.4168213 |  0.70158588 |\n",
       "| X7 |  0.34869847 |  0.41359462 | -0.13908580 | -0.17127417 | -0.20827738 | 0.41682128 |  1.0000000 |  0.39886792 |\n",
       "| X8 |  0.31867736 |  0.83495175 | -0.25835810 |  0.31275728 | -0.08123414 | 0.70158588 |  0.3988679 |  1.00000000 |\n",
       "\n"
      ],
      "text/plain": [
       "   X1          X2          X3          X4          X5          X6        \n",
       "X1  1.00000000  0.33364671 -0.05453868 -0.06125369 -0.28936059 0.19879627\n",
       "X2  0.33364671  1.00000000 -0.02290183  0.39893102 -0.15630387 0.71113407\n",
       "X3 -0.05453868 -0.02290183  1.00000000  0.53332919  0.49676279 0.03282961\n",
       "X4 -0.06125369  0.39893102  0.53332919  1.00000000  0.69842442 0.46791730\n",
       "X5 -0.28936059 -0.15630387  0.49676279  0.69842442  1.00000000 0.28012915\n",
       "X6  0.19879627  0.71113407  0.03282961  0.46791730  0.28012915 1.00000000\n",
       "X7  0.34869847  0.41359462 -0.13908580 -0.17127417 -0.20827738 0.41682128\n",
       "X8  0.31867736  0.83495175 -0.25835810  0.31275728 -0.08123414 0.70158588\n",
       "   X7         X8         \n",
       "X1  0.3486985  0.31867736\n",
       "X2  0.4135946  0.83495175\n",
       "X3 -0.1390858 -0.25835810\n",
       "X4 -0.1712742  0.31275728\n",
       "X5 -0.2082774 -0.08123414\n",
       "X6  0.4168213  0.70158588\n",
       "X7  1.0000000  0.39886792\n",
       "X8  0.3988679  1.00000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R <- cor(data); R"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "assisted-cornwall",
   "metadata": {},
   "source": [
    "## (2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "skilled-classroom",
   "metadata": {},
   "source": [
    "R 中用 `princomp` 来做 PCA，里面有个 `cor` 参数指定是否使用相关系数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "behavioral-duncan",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Importance of components:\n",
       "                         Comp.1    Comp.2    Comp.3     Comp.4     Comp.5\n",
       "Standard deviation     1.759627 1.5385783 0.9591597 0.84019364 0.70600448\n",
       "Proportion of Variance 0.387036 0.2959029 0.1149984 0.08824067 0.06230529\n",
       "Cumulative Proportion  0.387036 0.6829389 0.7979373 0.88617801 0.94848330\n",
       "                           Comp.6     Comp.7      Comp.8\n",
       "Standard deviation     0.47946669 0.36162932 0.226868982\n",
       "Proportion of Variance 0.02873604 0.01634697 0.006433692\n",
       "Cumulative Proportion  0.97721934 0.99356631 1.000000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca <- princomp(data, cor=TRUE)\n",
    "summary(pca)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "funny-rwanda",
   "metadata": {},
   "source": [
    "这里从 `summary` 输出中就有各主成分的贡献率 `Proportion of Variance`，\n",
    "以及累积贡献率 `Cumulative Proportion`。\n",
    "\n",
    "其中前两个主成分的累积贡献率为 $0.6829389$。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "conditional-lyric",
   "metadata": {},
   "source": [
    "这里可以作图来对 PCA 结果有更直观的感受："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "anticipated-marketing",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAYAAAD958/bAAAEDmlDQ1BrQ0dDb2xvclNwYWNl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\n4kVJzAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “pca”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(pca, type=\"lines\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "incorporated-tours",
   "metadata": {},
   "source": [
    "可以看到前两个主成分所占方差较大，所以只用前两个主成分就可以比较好的描述数据特征了。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "oriental-entrepreneur",
   "metadata": {},
   "source": [
    "## (3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "prescribed-playback",
   "metadata": {},
   "source": [
    "从 `pca$loading` 可以获取到个主成分的构成："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "liable-ancient",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Loadings:\n",
       "   Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8\n",
       "X1  0.250  0.241  0.694  0.377  0.502                     \n",
       "X2  0.519                0.225 -0.424         0.282  0.643\n",
       "X3        -0.475  0.578        -0.510  0.173 -0.381       \n",
       "X4  0.254 -0.538         0.231        -0.399  0.472 -0.458\n",
       "X5        -0.575        -0.285  0.516 -0.146 -0.159  0.521\n",
       "X6  0.493 -0.135 -0.145 -0.224  0.177  0.755        -0.244\n",
       "X7  0.317  0.261  0.286 -0.768        -0.355  0.131       \n",
       "X8  0.509        -0.271  0.177        -0.305 -0.708 -0.181\n",
       "\n",
       "               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8\n",
       "SS loadings     1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000\n",
       "Proportion Var  0.125  0.125  0.125  0.125  0.125  0.125  0.125  0.125\n",
       "Cumulative Var  0.125  0.250  0.375  0.500  0.625  0.750  0.875  1.000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca$loadings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "developmental-voltage",
   "metadata": {},
   "source": [
    "取出前两个主成分："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "realistic-tiger",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 8 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Comp.1</th><th scope=col>Comp.2</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td> 0.24960670</td><td> 0.24123818</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td> 0.51923425</td><td> 0.03760741</td></tr>\n",
       "\t<tr><th scope=row>X3</th><td>-0.01848008</td><td>-0.47543851</td></tr>\n",
       "\t<tr><th scope=row>X4</th><td> 0.25409160</td><td>-0.53808076</td></tr>\n",
       "\t<tr><th scope=row>X5</th><td> 0.02169482</td><td>-0.57544866</td></tr>\n",
       "\t<tr><th scope=row>X6</th><td> 0.49266309</td><td>-0.13467554</td></tr>\n",
       "\t<tr><th scope=row>X7</th><td> 0.31714669</td><td> 0.26068239</td></tr>\n",
       "\t<tr><th scope=row>X8</th><td> 0.50933155</td><td> 0.08708140</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 8 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & Comp.1 & Comp.2\\\\\n",
       "\\hline\n",
       "\tX1 &  0.24960670 &  0.24123818\\\\\n",
       "\tX2 &  0.51923425 &  0.03760741\\\\\n",
       "\tX3 & -0.01848008 & -0.47543851\\\\\n",
       "\tX4 &  0.25409160 & -0.53808076\\\\\n",
       "\tX5 &  0.02169482 & -0.57544866\\\\\n",
       "\tX6 &  0.49266309 & -0.13467554\\\\\n",
       "\tX7 &  0.31714669 &  0.26068239\\\\\n",
       "\tX8 &  0.50933155 &  0.08708140\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 8 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | Comp.1 | Comp.2 |\n",
       "|---|---|---|\n",
       "| X1 |  0.24960670 |  0.24123818 |\n",
       "| X2 |  0.51923425 |  0.03760741 |\n",
       "| X3 | -0.01848008 | -0.47543851 |\n",
       "| X4 |  0.25409160 | -0.53808076 |\n",
       "| X5 |  0.02169482 | -0.57544866 |\n",
       "| X6 |  0.49266309 | -0.13467554 |\n",
       "| X7 |  0.31714669 |  0.26068239 |\n",
       "| X8 |  0.50933155 |  0.08708140 |\n",
       "\n"
      ],
      "text/plain": [
       "   Comp.1      Comp.2     \n",
       "X1  0.24960670  0.24123818\n",
       "X2  0.51923425  0.03760741\n",
       "X3 -0.01848008 -0.47543851\n",
       "X4  0.25409160 -0.53808076\n",
       "X5  0.02169482 -0.57544866\n",
       "X6  0.49266309 -0.13467554\n",
       "X7  0.31714669  0.26068239\n",
       "X8  0.50933155  0.08708140"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca$loadings[,1:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "indirect-annotation",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y_1 =  0.25x_1+ 0.519x_2+ -0.018x_3+ 0.254x_4+ 0.022x_5+ 0.493x_6+ 0.317x_7+ 0.509x_8+ \n",
      "Y_2 =  0.241x_1+ 0.038x_2+ -0.475x_3+ -0.538x_4+ -0.575x_5+ -0.135x_6+ 0.261x_7+ 0.087x_8+ \n"
     ]
    }
   ],
   "source": [
    "cat(\"Y_1 = \", paste(round(pca$loadings[,1], 3), \"x_\", 1:8, \"+\", sep=\"\"), \"\\n\")\n",
    "cat(\"Y_2 = \", paste(round(pca$loadings[,2], 3), \"x_\", 1:8, \"+\", sep=\"\"), \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "laden-intention",
   "metadata": {},
   "source": [
    "即得到：\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "Y_1 &=  0.25x_1+ 0.519x_2 -0.018x_3+ 0.254x_4+ 0.022x_5+ 0.493x_6+ 0.317x_7+ 0.509x_8\\\\\n",
    "Y_2 &=  0.241x_1+ 0.038x_2 -0.475x_3 -0.538x_4 -0.575x_5 -0.135x_6+ 0.261x_7+ 0.087x_8\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "julian-behalf",
   "metadata": {},
   "source": [
    "- $Y_1$ 反映了各省人均消费水平，除烟茶酒（$X_3$）外，其他支出越高，其人均总体消费水平越高，而烟茶酒对其消费水平评价成负相关。\n",
    "- 在 $Y_2 $中人烟酒、其他副食、衣着、日用品系数为负；粮食、副食、燃料、非商品系数为正，说明 $Y_2$ 的绝对值越大，各省人均消费的在生活必需品与高档品差异越大。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "italian-hampton",
   "metadata": {},
   "source": [
    "`pca$scores` 可以获取在个主成分下数据的得分："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "complete-cargo",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 30 × 8 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Comp.1</th><th scope=col>Comp.2</th><th scope=col>Comp.3</th><th scope=col>Comp.4</th><th scope=col>Comp.5</th><th scope=col>Comp.6</th><th scope=col>Comp.7</th><th scope=col>Comp.8</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>山西</th><td>-1.71328041</td><td>-0.1702972</td><td>-0.16533704</td><td> 0.23590437</td><td> 0.569936490</td><td> 0.29875410</td><td>-0.48611208</td><td>-0.09116991</td></tr>\n",
       "\t<tr><th scope=row>内蒙古</th><td>-1.27970296</td><td> 0.1344973</td><td> 0.30689790</td><td>-0.23043192</td><td> 1.012468747</td><td> 0.07198599</td><td>-0.03717535</td><td>-0.12143528</td></tr>\n",
       "\t<tr><th scope=row>吉林</th><td>-1.31581695</td><td> 0.8750360</td><td>-0.11140786</td><td>-0.68616712</td><td> 0.247083948</td><td>-1.08443042</td><td> 0.57207381</td><td> 0.05978027</td></tr>\n",
       "\t<tr><th scope=row>黑龙江</th><td>-1.34833462</td><td> 0.1041418</td><td>-0.23606441</td><td>-1.22149653</td><td> 0.603997992</td><td>-0.91121622</td><td> 0.32415606</td><td> 0.48423086</td></tr>\n",
       "\t<tr><th scope=row>河南</th><td>-1.51135274</td><td> 0.3575657</td><td> 0.74485489</td><td> 0.15916151</td><td> 0.318199302</td><td> 0.22362082</td><td>-0.08877150</td><td> 0.06122241</td></tr>\n",
       "\t<tr><th scope=row>甘肃</th><td>-1.20243857</td><td> 0.1962559</td><td> 0.77061864</td><td> 0.03290876</td><td> 0.031513421</td><td>-0.17668219</td><td>-0.32211193</td><td>-0.21328633</td></tr>\n",
       "\t<tr><th scope=row>青海</th><td>-1.13238706</td><td> 0.0184613</td><td> 1.56666527</td><td> 0.16585236</td><td> 0.010877250</td><td>-0.35640196</td><td>-0.28908048</td><td>-0.16241711</td></tr>\n",
       "\t<tr><th scope=row>河北</th><td>-0.39890334</td><td> 0.3006773</td><td> 0.44000732</td><td>-0.76975727</td><td> 0.557414414</td><td>-0.25219732</td><td>-0.24503792</td><td>-0.29330670</td></tr>\n",
       "\t<tr><th scope=row>陕西</th><td>-0.62321145</td><td> 0.2873967</td><td>-0.03974784</td><td> 0.30778811</td><td> 0.905168787</td><td> 0.13749943</td><td> 0.12213088</td><td>-0.46191904</td></tr>\n",
       "\t<tr><th scope=row>宁夏</th><td>-0.43775323</td><td>-0.6567395</td><td>-0.14502865</td><td>-0.45256266</td><td> 1.065800286</td><td> 0.48700867</td><td>-0.17027760</td><td>-0.07691451</td></tr>\n",
       "\t<tr><th scope=row>新疆</th><td>-0.83249622</td><td> 0.4284772</td><td>-1.31216366</td><td>-0.52353448</td><td> 0.233313443</td><td>-0.33824264</td><td>-0.17043019</td><td>-0.25789460</td></tr>\n",
       "\t<tr><th scope=row>湖北</th><td>-0.17335839</td><td> 0.5996948</td><td> 0.13105793</td><td>-0.70785427</td><td> 0.102796108</td><td> 0.12846023</td><td>-0.30601657</td><td> 0.18738388</td></tr>\n",
       "\t<tr><th scope=row>云南</th><td>-0.67809647</td><td> 0.3005293</td><td> 0.22841114</td><td> 1.16558732</td><td> 0.547410479</td><td> 0.63752652</td><td>-0.04440406</td><td> 0.35660242</td></tr>\n",
       "\t<tr><th scope=row>湖南</th><td>-0.52687091</td><td> 0.5617115</td><td>-1.17427177</td><td>-0.22730234</td><td>-0.637516046</td><td> 0.19411512</td><td>-0.06581257</td><td>-0.09598281</td></tr>\n",
       "\t<tr><th scope=row>安徽</th><td>-1.13401837</td><td> 0.4479633</td><td> 0.22310249</td><td> 0.63162229</td><td>-1.135121996</td><td> 0.47275352</td><td>-0.19762601</td><td>-0.13391580</td></tr>\n",
       "\t<tr><th scope=row>贵州</th><td>-1.28087147</td><td> 0.4355961</td><td>-0.31186180</td><td> 0.42406853</td><td>-0.717322171</td><td>-0.42721526</td><td>-0.60824015</td><td> 0.19301087</td></tr>\n",
       "\t<tr><th scope=row>辽宁</th><td> 0.04597426</td><td>-0.9973278</td><td>-0.18880188</td><td>-0.39435146</td><td> 0.001524098</td><td>-0.53145394</td><td>-0.04009504</td><td> 0.24617664</td></tr>\n",
       "\t<tr><th scope=row>四川</th><td>-0.13719329</td><td>-0.3495031</td><td>-1.18966949</td><td> 0.16211927</td><td>-0.161510999</td><td> 0.57244188</td><td>-0.67692322</td><td> 0.37080157</td></tr>\n",
       "\t<tr><th scope=row>山东</th><td>-0.14352770</td><td>-0.6936321</td><td> 0.06841930</td><td>-0.54597236</td><td> 0.794096721</td><td> 0.96009874</td><td> 0.42746893</td><td> 0.01292320</td></tr>\n",
       "\t<tr><th scope=row>江西</th><td>-1.99443644</td><td> 2.1443095</td><td>-1.04918408</td><td>-0.09124788</td><td>-1.589855377</td><td>-0.30165950</td><td> 0.42014491</td><td>-0.34738661</td></tr>\n",
       "\t<tr><th scope=row>福建</th><td> 1.17362616</td><td> 1.3976957</td><td> 0.84741141</td><td> 0.73423571</td><td>-0.617905779</td><td> 0.02473358</td><td> 0.19700508</td><td> 0.01148641</td></tr>\n",
       "\t<tr><th scope=row>广西</th><td> 1.07457604</td><td> 1.2563578</td><td>-1.63199669</td><td>-0.07653990</td><td>-0.693330619</td><td> 0.86788824</td><td> 0.55704451</td><td>-0.06662925</td></tr>\n",
       "\t<tr><th scope=row>海南</th><td> 1.42511451</td><td> 3.2327307</td><td> 1.66191693</td><td> 1.96723103</td><td>-0.096122739</td><td>-0.30013866</td><td> 0.07821521</td><td> 0.19333947</td></tr>\n",
       "\t<tr><th scope=row>天津</th><td> 0.44287310</td><td>-0.4821918</td><td> 0.68627477</td><td> 1.26444816</td><td> 0.725655997</td><td> 0.11261393</td><td> 0.84478504</td><td> 0.12783423</td></tr>\n",
       "\t<tr><th scope=row>江苏</th><td> 0.15591226</td><td>-0.1151304</td><td>-0.52099459</td><td>-0.73836503</td><td>-0.693942745</td><td> 0.31633353</td><td> 0.41504815</td><td> 0.29813456</td></tr>\n",
       "\t<tr><th scope=row>浙江</th><td> 1.54097092</td><td>-1.3970121</td><td> 0.15434604</td><td>-1.09621902</td><td>-0.781850716</td><td> 0.04654020</td><td>-0.22375699</td><td> 0.25892031</td></tr>\n",
       "\t<tr><th scope=row>北京</th><td> 1.82277984</td><td>-2.9374614</td><td>-1.25748825</td><td> 0.55406973</td><td> 0.661967309</td><td>-0.22210262</td><td> 0.33005139</td><td>-0.14855873</td></tr>\n",
       "\t<tr><th scope=row>西藏</th><td>-0.13551813</td><td>-4.9923526</td><td> 2.37698478</td><td>-0.46230359</td><td>-1.441186117</td><td> 0.12998035</td><td> 0.22358976</td><td>-0.14715544</td></tr>\n",
       "\t<tr><th scope=row>上海</th><td> 3.30394931</td><td>-2.6047252</td><td>-1.70041148</td><td> 2.01766545</td><td>-0.031636936</td><td>-0.79913006</td><td>-0.29367453</td><td>-0.08851021</td></tr>\n",
       "\t<tr><th scope=row>广东</th><td> 7.01379233</td><td> 2.3172751</td><td> 0.82746069</td><td>-1.59855678</td><td> 0.208077446</td><td> 0.01851593</td><td>-0.24616755</td><td>-0.15536476</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 30 × 8 of type dbl\n",
       "\\begin{tabular}{r|llllllll}\n",
       "  & Comp.1 & Comp.2 & Comp.3 & Comp.4 & Comp.5 & Comp.6 & Comp.7 & Comp.8\\\\\n",
       "\\hline\n",
       "\t山西 & -1.71328041 & -0.1702972 & -0.16533704 &  0.23590437 &  0.569936490 &  0.29875410 & -0.48611208 & -0.09116991\\\\\n",
       "\t内蒙古 & -1.27970296 &  0.1344973 &  0.30689790 & -0.23043192 &  1.012468747 &  0.07198599 & -0.03717535 & -0.12143528\\\\\n",
       "\t吉林 & -1.31581695 &  0.8750360 & -0.11140786 & -0.68616712 &  0.247083948 & -1.08443042 &  0.57207381 &  0.05978027\\\\\n",
       "\t黑龙江 & -1.34833462 &  0.1041418 & -0.23606441 & -1.22149653 &  0.603997992 & -0.91121622 &  0.32415606 &  0.48423086\\\\\n",
       "\t河南 & -1.51135274 &  0.3575657 &  0.74485489 &  0.15916151 &  0.318199302 &  0.22362082 & -0.08877150 &  0.06122241\\\\\n",
       "\t甘肃 & -1.20243857 &  0.1962559 &  0.77061864 &  0.03290876 &  0.031513421 & -0.17668219 & -0.32211193 & -0.21328633\\\\\n",
       "\t青海 & -1.13238706 &  0.0184613 &  1.56666527 &  0.16585236 &  0.010877250 & -0.35640196 & -0.28908048 & -0.16241711\\\\\n",
       "\t河北 & -0.39890334 &  0.3006773 &  0.44000732 & -0.76975727 &  0.557414414 & -0.25219732 & -0.24503792 & -0.29330670\\\\\n",
       "\t陕西 & -0.62321145 &  0.2873967 & -0.03974784 &  0.30778811 &  0.905168787 &  0.13749943 &  0.12213088 & -0.46191904\\\\\n",
       "\t宁夏 & -0.43775323 & -0.6567395 & -0.14502865 & -0.45256266 &  1.065800286 &  0.48700867 & -0.17027760 & -0.07691451\\\\\n",
       "\t新疆 & -0.83249622 &  0.4284772 & -1.31216366 & -0.52353448 &  0.233313443 & -0.33824264 & -0.17043019 & -0.25789460\\\\\n",
       "\t湖北 & -0.17335839 &  0.5996948 &  0.13105793 & -0.70785427 &  0.102796108 &  0.12846023 & -0.30601657 &  0.18738388\\\\\n",
       "\t云南 & -0.67809647 &  0.3005293 &  0.22841114 &  1.16558732 &  0.547410479 &  0.63752652 & -0.04440406 &  0.35660242\\\\\n",
       "\t湖南 & -0.52687091 &  0.5617115 & -1.17427177 & -0.22730234 & -0.637516046 &  0.19411512 & -0.06581257 & -0.09598281\\\\\n",
       "\t安徽 & -1.13401837 &  0.4479633 &  0.22310249 &  0.63162229 & -1.135121996 &  0.47275352 & -0.19762601 & -0.13391580\\\\\n",
       "\t贵州 & -1.28087147 &  0.4355961 & -0.31186180 &  0.42406853 & -0.717322171 & -0.42721526 & -0.60824015 &  0.19301087\\\\\n",
       "\t辽宁 &  0.04597426 & -0.9973278 & -0.18880188 & -0.39435146 &  0.001524098 & -0.53145394 & -0.04009504 &  0.24617664\\\\\n",
       "\t四川 & -0.13719329 & -0.3495031 & -1.18966949 &  0.16211927 & -0.161510999 &  0.57244188 & -0.67692322 &  0.37080157\\\\\n",
       "\t山东 & -0.14352770 & -0.6936321 &  0.06841930 & -0.54597236 &  0.794096721 &  0.96009874 &  0.42746893 &  0.01292320\\\\\n",
       "\t江西 & -1.99443644 &  2.1443095 & -1.04918408 & -0.09124788 & -1.589855377 & -0.30165950 &  0.42014491 & -0.34738661\\\\\n",
       "\t福建 &  1.17362616 &  1.3976957 &  0.84741141 &  0.73423571 & -0.617905779 &  0.02473358 &  0.19700508 &  0.01148641\\\\\n",
       "\t广西 &  1.07457604 &  1.2563578 & -1.63199669 & -0.07653990 & -0.693330619 &  0.86788824 &  0.55704451 & -0.06662925\\\\\n",
       "\t海南 &  1.42511451 &  3.2327307 &  1.66191693 &  1.96723103 & -0.096122739 & -0.30013866 &  0.07821521 &  0.19333947\\\\\n",
       "\t天津 &  0.44287310 & -0.4821918 &  0.68627477 &  1.26444816 &  0.725655997 &  0.11261393 &  0.84478504 &  0.12783423\\\\\n",
       "\t江苏 &  0.15591226 & -0.1151304 & -0.52099459 & -0.73836503 & -0.693942745 &  0.31633353 &  0.41504815 &  0.29813456\\\\\n",
       "\t浙江 &  1.54097092 & -1.3970121 &  0.15434604 & -1.09621902 & -0.781850716 &  0.04654020 & -0.22375699 &  0.25892031\\\\\n",
       "\t北京 &  1.82277984 & -2.9374614 & -1.25748825 &  0.55406973 &  0.661967309 & -0.22210262 &  0.33005139 & -0.14855873\\\\\n",
       "\t西藏 & -0.13551813 & -4.9923526 &  2.37698478 & -0.46230359 & -1.441186117 &  0.12998035 &  0.22358976 & -0.14715544\\\\\n",
       "\t上海 &  3.30394931 & -2.6047252 & -1.70041148 &  2.01766545 & -0.031636936 & -0.79913006 & -0.29367453 & -0.08851021\\\\\n",
       "\t广东 &  7.01379233 &  2.3172751 &  0.82746069 & -1.59855678 &  0.208077446 &  0.01851593 & -0.24616755 & -0.15536476\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 30 × 8 of type dbl\n",
       "\n",
       "| <!--/--> | Comp.1 | Comp.2 | Comp.3 | Comp.4 | Comp.5 | Comp.6 | Comp.7 | Comp.8 |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 山西 | -1.71328041 | -0.1702972 | -0.16533704 |  0.23590437 |  0.569936490 |  0.29875410 | -0.48611208 | -0.09116991 |\n",
       "| 内蒙古 | -1.27970296 |  0.1344973 |  0.30689790 | -0.23043192 |  1.012468747 |  0.07198599 | -0.03717535 | -0.12143528 |\n",
       "| 吉林 | -1.31581695 |  0.8750360 | -0.11140786 | -0.68616712 |  0.247083948 | -1.08443042 |  0.57207381 |  0.05978027 |\n",
       "| 黑龙江 | -1.34833462 |  0.1041418 | -0.23606441 | -1.22149653 |  0.603997992 | -0.91121622 |  0.32415606 |  0.48423086 |\n",
       "| 河南 | -1.51135274 |  0.3575657 |  0.74485489 |  0.15916151 |  0.318199302 |  0.22362082 | -0.08877150 |  0.06122241 |\n",
       "| 甘肃 | -1.20243857 |  0.1962559 |  0.77061864 |  0.03290876 |  0.031513421 | -0.17668219 | -0.32211193 | -0.21328633 |\n",
       "| 青海 | -1.13238706 |  0.0184613 |  1.56666527 |  0.16585236 |  0.010877250 | -0.35640196 | -0.28908048 | -0.16241711 |\n",
       "| 河北 | -0.39890334 |  0.3006773 |  0.44000732 | -0.76975727 |  0.557414414 | -0.25219732 | -0.24503792 | -0.29330670 |\n",
       "| 陕西 | -0.62321145 |  0.2873967 | -0.03974784 |  0.30778811 |  0.905168787 |  0.13749943 |  0.12213088 | -0.46191904 |\n",
       "| 宁夏 | -0.43775323 | -0.6567395 | -0.14502865 | -0.45256266 |  1.065800286 |  0.48700867 | -0.17027760 | -0.07691451 |\n",
       "| 新疆 | -0.83249622 |  0.4284772 | -1.31216366 | -0.52353448 |  0.233313443 | -0.33824264 | -0.17043019 | -0.25789460 |\n",
       "| 湖北 | -0.17335839 |  0.5996948 |  0.13105793 | -0.70785427 |  0.102796108 |  0.12846023 | -0.30601657 |  0.18738388 |\n",
       "| 云南 | -0.67809647 |  0.3005293 |  0.22841114 |  1.16558732 |  0.547410479 |  0.63752652 | -0.04440406 |  0.35660242 |\n",
       "| 湖南 | -0.52687091 |  0.5617115 | -1.17427177 | -0.22730234 | -0.637516046 |  0.19411512 | -0.06581257 | -0.09598281 |\n",
       "| 安徽 | -1.13401837 |  0.4479633 |  0.22310249 |  0.63162229 | -1.135121996 |  0.47275352 | -0.19762601 | -0.13391580 |\n",
       "| 贵州 | -1.28087147 |  0.4355961 | -0.31186180 |  0.42406853 | -0.717322171 | -0.42721526 | -0.60824015 |  0.19301087 |\n",
       "| 辽宁 |  0.04597426 | -0.9973278 | -0.18880188 | -0.39435146 |  0.001524098 | -0.53145394 | -0.04009504 |  0.24617664 |\n",
       "| 四川 | -0.13719329 | -0.3495031 | -1.18966949 |  0.16211927 | -0.161510999 |  0.57244188 | -0.67692322 |  0.37080157 |\n",
       "| 山东 | -0.14352770 | -0.6936321 |  0.06841930 | -0.54597236 |  0.794096721 |  0.96009874 |  0.42746893 |  0.01292320 |\n",
       "| 江西 | -1.99443644 |  2.1443095 | -1.04918408 | -0.09124788 | -1.589855377 | -0.30165950 |  0.42014491 | -0.34738661 |\n",
       "| 福建 |  1.17362616 |  1.3976957 |  0.84741141 |  0.73423571 | -0.617905779 |  0.02473358 |  0.19700508 |  0.01148641 |\n",
       "| 广西 |  1.07457604 |  1.2563578 | -1.63199669 | -0.07653990 | -0.693330619 |  0.86788824 |  0.55704451 | -0.06662925 |\n",
       "| 海南 |  1.42511451 |  3.2327307 |  1.66191693 |  1.96723103 | -0.096122739 | -0.30013866 |  0.07821521 |  0.19333947 |\n",
       "| 天津 |  0.44287310 | -0.4821918 |  0.68627477 |  1.26444816 |  0.725655997 |  0.11261393 |  0.84478504 |  0.12783423 |\n",
       "| 江苏 |  0.15591226 | -0.1151304 | -0.52099459 | -0.73836503 | -0.693942745 |  0.31633353 |  0.41504815 |  0.29813456 |\n",
       "| 浙江 |  1.54097092 | -1.3970121 |  0.15434604 | -1.09621902 | -0.781850716 |  0.04654020 | -0.22375699 |  0.25892031 |\n",
       "| 北京 |  1.82277984 | -2.9374614 | -1.25748825 |  0.55406973 |  0.661967309 | -0.22210262 |  0.33005139 | -0.14855873 |\n",
       "| 西藏 | -0.13551813 | -4.9923526 |  2.37698478 | -0.46230359 | -1.441186117 |  0.12998035 |  0.22358976 | -0.14715544 |\n",
       "| 上海 |  3.30394931 | -2.6047252 | -1.70041148 |  2.01766545 | -0.031636936 | -0.79913006 | -0.29367453 | -0.08851021 |\n",
       "| 广东 |  7.01379233 |  2.3172751 |  0.82746069 | -1.59855678 |  0.208077446 |  0.01851593 | -0.24616755 | -0.15536476 |\n",
       "\n"
      ],
      "text/plain": [
       "                   Comp.1      Comp.2     Comp.3      Comp.4      Comp.5      \n",
       "\\u5c71\\u897f       -1.71328041 -0.1702972 -0.16533704  0.23590437  0.569936490\n",
       "\\u5185\\u8499\\u53e4 -1.27970296  0.1344973  0.30689790 -0.23043192  1.012468747\n",
       "\\u5409\\u6797       -1.31581695  0.8750360 -0.11140786 -0.68616712  0.247083948\n",
       "\\u9ed1\\u9f99\\u6c5f -1.34833462  0.1041418 -0.23606441 -1.22149653  0.603997992\n",
       "\\u6cb3\\u5357       -1.51135274  0.3575657  0.74485489  0.15916151  0.318199302\n",
       "\\u7518\\u8083       -1.20243857  0.1962559  0.77061864  0.03290876  0.031513421\n",
       "\\u9752\\u6d77       -1.13238706  0.0184613  1.56666527  0.16585236  0.010877250\n",
       "\\u6cb3\\u5317       -0.39890334  0.3006773  0.44000732 -0.76975727  0.557414414\n",
       "\\u9655\\u897f       -0.62321145  0.2873967 -0.03974784  0.30778811  0.905168787\n",
       "\\u5b81\\u590f       -0.43775323 -0.6567395 -0.14502865 -0.45256266  1.065800286\n",
       "\\u65b0\\u7586       -0.83249622  0.4284772 -1.31216366 -0.52353448  0.233313443\n",
       "\\u6e56\\u5317       -0.17335839  0.5996948  0.13105793 -0.70785427  0.102796108\n",
       "\\u4e91\\u5357       -0.67809647  0.3005293  0.22841114  1.16558732  0.547410479\n",
       "\\u6e56\\u5357       -0.52687091  0.5617115 -1.17427177 -0.22730234 -0.637516046\n",
       "\\u5b89\\u5fbd       -1.13401837  0.4479633  0.22310249  0.63162229 -1.135121996\n",
       "\\u8d35\\u5dde       -1.28087147  0.4355961 -0.31186180  0.42406853 -0.717322171\n",
       "\\u8fbd\\u5b81        0.04597426 -0.9973278 -0.18880188 -0.39435146  0.001524098\n",
       "\\u56db\\u5ddd       -0.13719329 -0.3495031 -1.18966949  0.16211927 -0.161510999\n",
       "\\u5c71\\u4e1c       -0.14352770 -0.6936321  0.06841930 -0.54597236  0.794096721\n",
       "\\u6c5f\\u897f       -1.99443644  2.1443095 -1.04918408 -0.09124788 -1.589855377\n",
       "\\u798f\\u5efa        1.17362616  1.3976957  0.84741141  0.73423571 -0.617905779\n",
       "\\u5e7f\\u897f        1.07457604  1.2563578 -1.63199669 -0.07653990 -0.693330619\n",
       "\\u6d77\\u5357        1.42511451  3.2327307  1.66191693  1.96723103 -0.096122739\n",
       "\\u5929\\u6d25        0.44287310 -0.4821918  0.68627477  1.26444816  0.725655997\n",
       "\\u6c5f\\u82cf        0.15591226 -0.1151304 -0.52099459 -0.73836503 -0.693942745\n",
       "\\u6d59\\u6c5f        1.54097092 -1.3970121  0.15434604 -1.09621902 -0.781850716\n",
       "\\u5317\\u4eac        1.82277984 -2.9374614 -1.25748825  0.55406973  0.661967309\n",
       "\\u897f\\u85cf       -0.13551813 -4.9923526  2.37698478 -0.46230359 -1.441186117\n",
       "\\u4e0a\\u6d77        3.30394931 -2.6047252 -1.70041148  2.01766545 -0.031636936\n",
       "\\u5e7f\\u4e1c        7.01379233  2.3172751  0.82746069 -1.59855678  0.208077446\n",
       "                   Comp.6      Comp.7      Comp.8     \n",
       "\\u5c71\\u897f        0.29875410 -0.48611208 -0.09116991\n",
       "\\u5185\\u8499\\u53e4  0.07198599 -0.03717535 -0.12143528\n",
       "\\u5409\\u6797       -1.08443042  0.57207381  0.05978027\n",
       "\\u9ed1\\u9f99\\u6c5f -0.91121622  0.32415606  0.48423086\n",
       "\\u6cb3\\u5357        0.22362082 -0.08877150  0.06122241\n",
       "\\u7518\\u8083       -0.17668219 -0.32211193 -0.21328633\n",
       "\\u9752\\u6d77       -0.35640196 -0.28908048 -0.16241711\n",
       "\\u6cb3\\u5317       -0.25219732 -0.24503792 -0.29330670\n",
       "\\u9655\\u897f        0.13749943  0.12213088 -0.46191904\n",
       "\\u5b81\\u590f        0.48700867 -0.17027760 -0.07691451\n",
       "\\u65b0\\u7586       -0.33824264 -0.17043019 -0.25789460\n",
       "\\u6e56\\u5317        0.12846023 -0.30601657  0.18738388\n",
       "\\u4e91\\u5357        0.63752652 -0.04440406  0.35660242\n",
       "\\u6e56\\u5357        0.19411512 -0.06581257 -0.09598281\n",
       "\\u5b89\\u5fbd        0.47275352 -0.19762601 -0.13391580\n",
       "\\u8d35\\u5dde       -0.42721526 -0.60824015  0.19301087\n",
       "\\u8fbd\\u5b81       -0.53145394 -0.04009504  0.24617664\n",
       "\\u56db\\u5ddd        0.57244188 -0.67692322  0.37080157\n",
       "\\u5c71\\u4e1c        0.96009874  0.42746893  0.01292320\n",
       "\\u6c5f\\u897f       -0.30165950  0.42014491 -0.34738661\n",
       "\\u798f\\u5efa        0.02473358  0.19700508  0.01148641\n",
       "\\u5e7f\\u897f        0.86788824  0.55704451 -0.06662925\n",
       "\\u6d77\\u5357       -0.30013866  0.07821521  0.19333947\n",
       "\\u5929\\u6d25        0.11261393  0.84478504  0.12783423\n",
       "\\u6c5f\\u82cf        0.31633353  0.41504815  0.29813456\n",
       "\\u6d59\\u6c5f        0.04654020 -0.22375699  0.25892031\n",
       "\\u5317\\u4eac       -0.22210262  0.33005139 -0.14855873\n",
       "\\u897f\\u85cf        0.12998035  0.22358976 -0.14715544\n",
       "\\u4e0a\\u6d77       -0.79913006 -0.29367453 -0.08851021\n",
       "\\u5e7f\\u4e1c        0.01851593 -0.24616755 -0.15536476"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca$scores"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "atomic-immune",
   "metadata": {},
   "source": [
    "从中我们获取的一主成分的得分，并进行排序："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "sufficient-shirt",
   "metadata": {},
   "outputs": [],
   "source": [
    "Comp.1.scores <- pca$scores[,1]\n",
    "Comp.1.scores.sorted <- Comp.1.scores[order(Comp.1.scores, decreasing = TRUE)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "economic-cornwall",
   "metadata": {},
   "source": [
    "为了好看，稍微处理一下结果再输出："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "acceptable-corps",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 30 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>idx</th><th scope=col>Comp.1.scores.sorted</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>广东</th><td> 1</td><td> 7.01379233</td></tr>\n",
       "\t<tr><th scope=row>上海</th><td> 2</td><td> 3.30394931</td></tr>\n",
       "\t<tr><th scope=row>北京</th><td> 3</td><td> 1.82277984</td></tr>\n",
       "\t<tr><th scope=row>浙江</th><td> 4</td><td> 1.54097092</td></tr>\n",
       "\t<tr><th scope=row>海南</th><td> 5</td><td> 1.42511451</td></tr>\n",
       "\t<tr><th scope=row>福建</th><td> 6</td><td> 1.17362616</td></tr>\n",
       "\t<tr><th scope=row>广西</th><td> 7</td><td> 1.07457604</td></tr>\n",
       "\t<tr><th scope=row>天津</th><td> 8</td><td> 0.44287310</td></tr>\n",
       "\t<tr><th scope=row>江苏</th><td> 9</td><td> 0.15591226</td></tr>\n",
       "\t<tr><th scope=row>辽宁</th><td>10</td><td> 0.04597426</td></tr>\n",
       "\t<tr><th scope=row>西藏</th><td>11</td><td>-0.13551813</td></tr>\n",
       "\t<tr><th scope=row>四川</th><td>12</td><td>-0.13719329</td></tr>\n",
       "\t<tr><th scope=row>山东</th><td>13</td><td>-0.14352770</td></tr>\n",
       "\t<tr><th scope=row>湖北</th><td>14</td><td>-0.17335839</td></tr>\n",
       "\t<tr><th scope=row>河北</th><td>15</td><td>-0.39890334</td></tr>\n",
       "\t<tr><th scope=row>宁夏</th><td>16</td><td>-0.43775323</td></tr>\n",
       "\t<tr><th scope=row>湖南</th><td>17</td><td>-0.52687091</td></tr>\n",
       "\t<tr><th scope=row>陕西</th><td>18</td><td>-0.62321145</td></tr>\n",
       "\t<tr><th scope=row>云南</th><td>19</td><td>-0.67809647</td></tr>\n",
       "\t<tr><th scope=row>新疆</th><td>20</td><td>-0.83249622</td></tr>\n",
       "\t<tr><th scope=row>青海</th><td>21</td><td>-1.13238706</td></tr>\n",
       "\t<tr><th scope=row>安徽</th><td>22</td><td>-1.13401837</td></tr>\n",
       "\t<tr><th scope=row>甘肃</th><td>23</td><td>-1.20243857</td></tr>\n",
       "\t<tr><th scope=row>内蒙古</th><td>24</td><td>-1.27970296</td></tr>\n",
       "\t<tr><th scope=row>贵州</th><td>25</td><td>-1.28087147</td></tr>\n",
       "\t<tr><th scope=row>吉林</th><td>26</td><td>-1.31581695</td></tr>\n",
       "\t<tr><th scope=row>黑龙江</th><td>27</td><td>-1.34833462</td></tr>\n",
       "\t<tr><th scope=row>河南</th><td>28</td><td>-1.51135274</td></tr>\n",
       "\t<tr><th scope=row>山西</th><td>29</td><td>-1.71328041</td></tr>\n",
       "\t<tr><th scope=row>江西</th><td>30</td><td>-1.99443644</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 30 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & idx & Comp.1.scores.sorted\\\\\n",
       "  & <int> & <dbl>\\\\\n",
       "\\hline\n",
       "\t广东 &  1 &  7.01379233\\\\\n",
       "\t上海 &  2 &  3.30394931\\\\\n",
       "\t北京 &  3 &  1.82277984\\\\\n",
       "\t浙江 &  4 &  1.54097092\\\\\n",
       "\t海南 &  5 &  1.42511451\\\\\n",
       "\t福建 &  6 &  1.17362616\\\\\n",
       "\t广西 &  7 &  1.07457604\\\\\n",
       "\t天津 &  8 &  0.44287310\\\\\n",
       "\t江苏 &  9 &  0.15591226\\\\\n",
       "\t辽宁 & 10 &  0.04597426\\\\\n",
       "\t西藏 & 11 & -0.13551813\\\\\n",
       "\t四川 & 12 & -0.13719329\\\\\n",
       "\t山东 & 13 & -0.14352770\\\\\n",
       "\t湖北 & 14 & -0.17335839\\\\\n",
       "\t河北 & 15 & -0.39890334\\\\\n",
       "\t宁夏 & 16 & -0.43775323\\\\\n",
       "\t湖南 & 17 & -0.52687091\\\\\n",
       "\t陕西 & 18 & -0.62321145\\\\\n",
       "\t云南 & 19 & -0.67809647\\\\\n",
       "\t新疆 & 20 & -0.83249622\\\\\n",
       "\t青海 & 21 & -1.13238706\\\\\n",
       "\t安徽 & 22 & -1.13401837\\\\\n",
       "\t甘肃 & 23 & -1.20243857\\\\\n",
       "\t内蒙古 & 24 & -1.27970296\\\\\n",
       "\t贵州 & 25 & -1.28087147\\\\\n",
       "\t吉林 & 26 & -1.31581695\\\\\n",
       "\t黑龙江 & 27 & -1.34833462\\\\\n",
       "\t河南 & 28 & -1.51135274\\\\\n",
       "\t山西 & 29 & -1.71328041\\\\\n",
       "\t江西 & 30 & -1.99443644\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 30 × 2\n",
       "\n",
       "| <!--/--> | idx &lt;int&gt; | Comp.1.scores.sorted &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 广东 |  1 |  7.01379233 |\n",
       "| 上海 |  2 |  3.30394931 |\n",
       "| 北京 |  3 |  1.82277984 |\n",
       "| 浙江 |  4 |  1.54097092 |\n",
       "| 海南 |  5 |  1.42511451 |\n",
       "| 福建 |  6 |  1.17362616 |\n",
       "| 广西 |  7 |  1.07457604 |\n",
       "| 天津 |  8 |  0.44287310 |\n",
       "| 江苏 |  9 |  0.15591226 |\n",
       "| 辽宁 | 10 |  0.04597426 |\n",
       "| 西藏 | 11 | -0.13551813 |\n",
       "| 四川 | 12 | -0.13719329 |\n",
       "| 山东 | 13 | -0.14352770 |\n",
       "| 湖北 | 14 | -0.17335839 |\n",
       "| 河北 | 15 | -0.39890334 |\n",
       "| 宁夏 | 16 | -0.43775323 |\n",
       "| 湖南 | 17 | -0.52687091 |\n",
       "| 陕西 | 18 | -0.62321145 |\n",
       "| 云南 | 19 | -0.67809647 |\n",
       "| 新疆 | 20 | -0.83249622 |\n",
       "| 青海 | 21 | -1.13238706 |\n",
       "| 安徽 | 22 | -1.13401837 |\n",
       "| 甘肃 | 23 | -1.20243857 |\n",
       "| 内蒙古 | 24 | -1.27970296 |\n",
       "| 贵州 | 25 | -1.28087147 |\n",
       "| 吉林 | 26 | -1.31581695 |\n",
       "| 黑龙江 | 27 | -1.34833462 |\n",
       "| 河南 | 28 | -1.51135274 |\n",
       "| 山西 | 29 | -1.71328041 |\n",
       "| 江西 | 30 | -1.99443644 |\n",
       "\n"
      ],
      "text/plain": [
       "                   idx Comp.1.scores.sorted\n",
       "\\u5e7f\\u4e1c        1   7.01379233         \n",
       "\\u4e0a\\u6d77        2   3.30394931         \n",
       "\\u5317\\u4eac        3   1.82277984         \n",
       "\\u6d59\\u6c5f        4   1.54097092         \n",
       "\\u6d77\\u5357        5   1.42511451         \n",
       "\\u798f\\u5efa        6   1.17362616         \n",
       "\\u5e7f\\u897f        7   1.07457604         \n",
       "\\u5929\\u6d25        8   0.44287310         \n",
       "\\u6c5f\\u82cf        9   0.15591226         \n",
       "\\u8fbd\\u5b81       10   0.04597426         \n",
       "\\u897f\\u85cf       11  -0.13551813         \n",
       "\\u56db\\u5ddd       12  -0.13719329         \n",
       "\\u5c71\\u4e1c       13  -0.14352770         \n",
       "\\u6e56\\u5317       14  -0.17335839         \n",
       "\\u6cb3\\u5317       15  -0.39890334         \n",
       "\\u5b81\\u590f       16  -0.43775323         \n",
       "\\u6e56\\u5357       17  -0.52687091         \n",
       "\\u9655\\u897f       18  -0.62321145         \n",
       "\\u4e91\\u5357       19  -0.67809647         \n",
       "\\u65b0\\u7586       20  -0.83249622         \n",
       "\\u9752\\u6d77       21  -1.13238706         \n",
       "\\u5b89\\u5fbd       22  -1.13401837         \n",
       "\\u7518\\u8083       23  -1.20243857         \n",
       "\\u5185\\u8499\\u53e4 24  -1.27970296         \n",
       "\\u8d35\\u5dde       25  -1.28087147         \n",
       "\\u5409\\u6797       26  -1.31581695         \n",
       "\\u9ed1\\u9f99\\u6c5f 27  -1.34833462         \n",
       "\\u6cb3\\u5357       28  -1.51135274         \n",
       "\\u5c71\\u897f       29  -1.71328041         \n",
       "\\u6c5f\\u897f       30  -1.99443644         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx <- 1:length(Comp.1.scores.sorted)\n",
    "cbind(idx, data.frame(Comp.1.scores.sorted))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.0.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
